A reaction is represented by this equation: \(2 \mathrm{W}(a q) \rightleftharpoons \mathrm{X}(a q)+2 \mathrm{Y}(a q) \quad K_{c}=5 \times 10^{-4}\) (a) Write the mathematical expression for the equilibrium constant. (b) Using concentrations of \(\leq 1 M,\) identify two sets of concentrations that describe a mixture of \(\mathrm{W}, \mathrm{X},\) and \(\mathrm{Y}\) at equilibrium.

Understanding the equilibrium constant expression is critical when studying chemical equilibrium. It is a way to quantify the extent of a reaction, or in simple terms, to tell us how far a reaction will go before reaching equilibrium. The equilibrium constant, represented by Kc for reactions in solution or Kp for reactions involving gases, is calculated from the concentrations (or partial pressures) of the products and reactants.

For a reaction at equilibrium, the expression is derived by taking the product of the concentrations of the products, each raised to the power of their stoichiometric coefficient, and dividing this by the product of the concentrations of the reactants, each also raised to their stoichiometric coefficient. This is symbolized in the equation \[ K_c = \frac{[\text{products}]^{\text{coefficients}}}{[\text{reactants}]^{\text{coefficients}}} \] In practice, this means that if a reaction has reached equilibrium at a certain temperature, the ratio of the concentration of the products to reactants will remain constant, represented by the equilibrium constant.

Stoichiometry is the section of chemistry that involves using relationships between reactants and products in a chemical reaction to predict quantities of either reactants or products. It's like a mathematical recipe for a chemical reaction telling us how much of each substance we need to make a certain amount of another substance or how much we produce from a given amount of reactants.

The stoichiometric coefficients are the numbers in front of the chemical species in a balanced chemical equation and indicate the ratios in which reactants combine and products form. When applying stoichiometry to equilibria, these coefficients are crucial as they are used as exponents in the equilibrium expression. They tell you how the concentration of each reactant and product influences the position of equilibrium.

Calculating the equilibrium concentration of substances in a reaction involves using the equilibrium constant expression along with the stoichiometry of the reaction. By understanding the chemical equation and the value of the equilibrium constant, we can calculate unknown concentrations at equilibrium given some concentrations.

It's a bit like a puzzle where you must use clues (the given concentrations and Kc) to find the missing pieces (the unknown concentrations). This involves algebraic manipulations, where you substitute known values into the equilibrium expression and solve for the unknowns. Having the right stoichiometry for each substance is key here, as any mistake will lead to incorrect results.

Reversible reactions are those that can proceed in both forward and reverse directions. In other words, the products can re-form the original reactants. When a reversible reaction is allowed to proceed in a closed system without interference, it will eventually reach a state of balance, or equilibrium, where the rate of the forward reaction equals the rate of the reverse reaction.

This does not mean that the reaction has stopped; rather, the concentrations of reactants and products remain constant over time. It’s a dynamic balance, as reactants continue to form products at the same rate that products break down into reactants. This concept greatly influences how we predict the behavior of a reaction and calculate the equilibrium concentrations of the involved substances.